Which expression is equivalent to ?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
3. Unit Circle
Trigonometric Functions on the Unit Circle
Multiple Choice
For the function on the unit circle, what is its minimum value?
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Verified step by step guidance1
Recall that the function given is \(f(x) = \sin(x)\), which represents the sine of an angle \(x\) measured in radians on the unit circle.
Understand that the sine function corresponds to the y-coordinate of a point on the unit circle as the angle \(x\) varies from \(0\) to \(2\pi\) radians (or \(0\) to \(360^\circ\)).
Know the range of the sine function: since it represents the vertical coordinate on the unit circle, its values always lie between \(-1\) and \(1\), inclusive.
Identify the minimum value of \(\sin(x)\) by considering the lowest point on the unit circle's vertical axis, which occurs at the angle \(x = \frac{3\pi}{2}\) radians (or \(270^\circ\)), where the sine value is \(-1\).
Conclude that the minimum value of \(f(x) = \sin(x)\) on the unit circle is \(-1\).
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